Code
knitr::opts_chunk$set(echo = TRUE)
library(caTools) # external package providing write.gif function
jet.colors <- colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F",
"yellow", "#FF7F00", "red", "#7F0000"))
dx <- 400 # define width
dy <- 400 # define height
C <- complex( real=rep(seq(-2.2, 1.0, length.out=dx), each=dy ),
imag=rep(seq(-1.2, 1.2, length.out=dy), dx ) )
C <- matrix(C,dy,dx) # reshape as square matrix of complex numbers
Z1 <- 0 # initialize Z to zero
Z2 <- 0
X1 <- array(0, c(dy,dx,100)) # initialize output 3D array
X2 <- X1
for (k in 1:100) { # loop with 20 iterations
Z1 <- Z1^2 + C # the central difference equation
Z2 <- Z2^4 + C
X1[,,k] <- exp(-abs(Z1)) # capture results
X2[,,k] <- exp(-abs(Z2))
}
write.gif(X1, "Mandelbrot222.gif", col=jet.colors, delay=100)
write.gif(X2, "Mandelbrot333.gif", col=jet.colors, delay=100)
Results
Mandelbrot set ( \(z = z^2 + c\))
Another fractal (\(z = z^4 + c\))
